I've done my own lawn of about 12000 sq ft for years and found the
basic Scotts Speedy Green type rotary spreaders that go for about $45
perfectly adequate. Not sure it's worth it to spend more money to do a
1/4 acre. Mine is 10 years old now and still works fine.

For spraying, I use either a 2 gallon tank type that you can fill with
water and pressurize at the same time from a garden hose (also has a
hand pump), or for bigger jobs a backpack sprayer that has a hand pump
on the side and various spray nozzles. Once you have the lawn under
control, and good turf established, all that should be needed is
occasional spot treatment for weed control. I use the small sprayer to
kill weeds in beds too. For the lawn, a 2 gallon tank full of
herbicide is enough for a couple of treatments, lasts maybe 6 weeks.

I fertilize twice. Once with pre-emergent crabgrass control/fertilizer
in Spring, then once in early Sept, again in mid Oct.